MinT - Best Known (110−60, 110, s)-Nets in Base 32

Best Known (110−60, 110, s)-Nets in Base 32

(110−60, 110, 224)-Net over F₃₂ — Constructive and digital

Digital (50, 110, 224)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 39, 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, 71, 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]

(110−60, 110, 464)-Net over F₃₂ — Digital

Digital (50, 110, 464)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−60, 110, 513)-Net in Base 32 — Constructive

(50, 110, 513)-net in base 32, using

32² times duplication [i] based on (48, 108, 513)-net in base 32, using
- t-expansion [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 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]

(110−60, 110, 128309)-Net in Base 32 — Upper bound on s

There is no (50, 110, 128310)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3686 178627 368687 347443 412996 893947 964197 000164 249819 130233 361150 822301 106112 167178 487994 929001 384135 113943 629643 567598 752516 570332 915883 638319 540906 242648 630501 640272 > 32¹¹⁰ [i]