MinT - Best Known (63, 63+141, s)-Nets in Base 4

Best Known (63, 63+141, s)-Nets in Base 4

(63, 63+141, 66)-Net over F₄ — Constructive and digital

Digital (63, 204, 66)-net over F₄, using

t-expansion [i] based on digital (49, 204, 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+141, 99)-Net over F₄ — Digital

Digital (63, 204, 99)-net over F₄, using

t-expansion [i] based on digital (61, 204, 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+141, 444)-Net in Base 4 — Upper bound on s

There is no (63, 204, 445)-net in base 4, because

1 times m-reduction [i] would yield (63, 203, 445)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 187 889463 633266 345676 829462 944519 142857 184899 345528 636279 995147 042711 472310 974451 606646 948044 584354 751841 805036 325691 636152 > 4²⁰³ [i]