MinT - Best Known (63, 63+142, s)-Nets in Base 4

Best Known (63, 63+142, s)-Nets in Base 4

(63, 63+142, 66)-Net over F₄ — Constructive and digital

Digital (63, 205, 66)-net over F₄, using

t-expansion [i] based on digital (49, 205, 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, 63+142, 99)-Net over F₄ — Digital

Digital (63, 205, 99)-net over F₄, using

t-expansion [i] based on digital (61, 205, 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, 63+142, 441)-Net in Base 4 — Upper bound on s

There is no (63, 205, 442)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2887 158303 380750 212080 935919 607041 359227 090780 111819 829361 077532 450257 095030 522114 986471 735589 502418 397382 195347 169524 682584 > 4²⁰⁵ [i]