MinT - Best Known (63, 177, s)-Nets in Base 4

Best Known (63, 177, s)-Nets in Base 4

(63, 177, 66)-Net over F₄ — Constructive and digital

Digital (63, 177, 66)-net over F₄, using

t-expansion [i] based on digital (49, 177, 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]

(63, 177, 99)-Net over F₄ — Digital

Digital (63, 177, 99)-net over F₄, using

t-expansion [i] based on digital (61, 177, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(63, 177, 499)-Net in Base 4 — Upper bound on s

There is no (63, 177, 500)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38577 020115 672800 469868 221098 254921 636631 554670 301767 238728 476584 426580 148359 941749 432446 052420 853409 504936 > 4¹⁷⁷ [i]