MinT - Best Known (246−141, 246, s)-Nets in Base 4

Best Known (246−141, 246, s)-Nets in Base 4

(246−141, 246, 130)-Net over F₄ — Constructive and digital

Digital (105, 246, 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]

(246−141, 246, 144)-Net over F₄ — Digital

Digital (105, 246, 144)-net over F₄, using

t-expansion [i] based on digital (91, 246, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(246−141, 246, 1090)-Net in Base 4 — Upper bound on s

There is no (105, 246, 1091)-net in base 4, because

1 times m-reduction [i] would yield (105, 245, 1091)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3231 360472 173784 282348 558469 640753 000109 702853 662838 409363 829715 501298 679099 265380 645983 539256 339090 564664 608610 520244 557070 915092 859103 559227 002880 > 4²⁴⁵ [i]