MinT - Best Known (125, 256, s)-Nets in Base 4

Best Known (125, 256, s)-Nets in Base 4

(125, 256, 130)-Net over F₄ — Constructive and digital

Digital (125, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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]

(125, 256, 176)-Net over F₄ — Digital

Digital (125, 256, 176)-net over F₄, using

net from sequence [i] based on digital (125, 175)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 125 and N(F) ≥ 176, using
  - Drinfeld modules of rank 1 [i]

(125, 256, 1867)-Net in Base 4 — Upper bound on s

There is no (125, 256, 1868)-net in base 4, because

1 times m-reduction [i] would yield (125, 255, 1868)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3367 708702 595588 226867 992157 309573 461671 897536 410647 445932 047395 912974 978568 046780 643676 161100 532663 881346 680236 622040 900396 043712 468298 280434 100916 106337 > 4²⁵⁵ [i]