MinT - Best Known (93−49, 93, s)-Nets in Base 32

Best Known (93−49, 93, s)-Nets in Base 32

(93−49, 93, 224)-Net over F₃₂ — Constructive and digital

Digital (44, 93, 224)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 33, 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, 60, 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]

(93−49, 93, 503)-Net over F₃₂ — Digital

Digital (44, 93, 503)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−49, 93, 513)-Net in Base 32 — Constructive

(44, 93, 513)-net in base 32, using

3 times m-reduction [i] based on (44, 96, 513)-net in base 32, using
- base change [i] based on digital (28, 80, 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]

(93−49, 93, 186086)-Net in Base 32 — Upper bound on s

There is no (44, 93, 186087)-net in base 32, because

1 times m-reduction [i] would yield (44, 92, 186087)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 977469 188865 491938 486495 951889 786971 114264 942253 778323 508934 269968 838157 095607 591749 497411 388590 715574 240468 973291 147999 135380 845014 895452 > 32⁹² [i]