MinT - Best Known (221−111, 221, s)-Nets in Base 4

Best Known (221−111, 221, s)-Nets in Base 4

(221−111, 221, 130)-Net over F₄ — Constructive and digital

Digital (110, 221, 130)-net over F₄, using

t-expansion [i] based on digital (105, 221, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(221−111, 221, 165)-Net over F₄ — Digital

Digital (110, 221, 165)-net over F₄, using

t-expansion [i] based on digital (109, 221, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(221−111, 221, 1775)-Net in Base 4 — Upper bound on s

There is no (110, 221, 1776)-net in base 4, because

1 times m-reduction [i] would yield (110, 220, 1776)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 843287 034134 443075 147490 339845 667304 452869 622835 906849 395061 448676 621241 323052 636740 896446 592310 889113 164582 636713 754683 377178 994460 > 4²²⁰ [i]