MinT - Best Known (189−83, 189, s)-Nets in Base 4

Best Known (189−83, 189, s)-Nets in Base 4

(189−83, 189, 130)-Net over F₄ — Constructive and digital

Digital (106, 189, 130)-net over F₄, using

t-expansion [i] based on digital (105, 189, 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]

(189−83, 189, 206)-Net over F₄ — Digital

Digital (106, 189, 206)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−83, 189, 3067)-Net in Base 4 — Upper bound on s

There is no (106, 189, 3068)-net in base 4, because

1 times m-reduction [i] would yield (106, 188, 3068)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 155647 825433 383294 626183 865487 952881 344280 324883 034469 922762 323816 478039 268360 363538 896881 468867 473511 826311 049075 > 4¹⁸⁸ [i]