MinT - Best Known (45, 94, s)-Nets in Base 32

Best Known (45, 94, s)-Nets in Base 32

(45, 94, 224)-Net over F₃₂ — Constructive and digital

Digital (45, 94, 224)-net over F₃₂, using

1 times m-reduction [i] based on digital (45, 95, 224)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 34, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]
  2. digital (11, 61, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(45, 94, 513)-Net in Base 32 — Constructive

(45, 94, 513)-net in base 32, using

8 times m-reduction [i] based on (45, 102, 513)-net in base 32, using
- base change [i] based on digital (28, 85, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(45, 94, 543)-Net over F₃₂ — Digital

Digital (45, 94, 543)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 94, 214997)-Net in Base 32 — Upper bound on s

There is no (45, 94, 214998)-net in base 32, because

1 times m-reduction [i] would yield (45, 93, 214998)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 95 278757 942920 753341 412969 040514 142858 782728 239988 146512 176865 650283 681967 579694 428600 230597 020184 011284 720240 405745 244592 322438 148913 883624 > 32⁹³ [i]