MinT - Best Known (237−107, 237, s)-Nets in Base 4

Best Known (237−107, 237, s)-Nets in Base 4

(237−107, 237, 130)-Net over F₄ — Constructive and digital

Digital (130, 237, 130)-net over F₄, using

t-expansion [i] based on digital (105, 237, 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]

(237−107, 237, 230)-Net over F₄ — Digital

Digital (130, 237, 230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−107, 237, 3249)-Net in Base 4 — Upper bound on s

There is no (130, 237, 3250)-net in base 4, because

1 times m-reduction [i] would yield (130, 236, 3250)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12359 091937 915135 437365 002279 728844 632363 380389 543635 025081 038349 114081 993386 661913 050236 845789 333150 984389 475788 452341 584263 154059 239916 512416 > 4²³⁶ [i]