MinT - Best Known (51, 51+94, s)-Nets in Base 4

Best Known (51, 51+94, s)-Nets in Base 4

(51, 51+94, 66)-Net over F₄ — Constructive and digital

Digital (51, 145, 66)-net over F₄, using

t-expansion [i] based on digital (49, 145, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(51, 51+94, 91)-Net over F₄ — Digital

Digital (51, 145, 91)-net over F₄, using

t-expansion [i] based on digital (50, 145, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(51, 51+94, 403)-Net in Base 4 — Upper bound on s

There is no (51, 145, 404)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2091 172121 524622 948498 069573 087795 810726 194665 840372 981449 435418 099036 836018 088577 402480 > 4¹⁴⁵ [i]