MinT - Best Known (137, 137+115, s)-Nets in Base 4

Best Known (137, 137+115, s)-Nets in Base 4

(137, 137+115, 130)-Net over F₄ — Constructive and digital

Digital (137, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(137, 137+115, 235)-Net over F₄ — Digital

Digital (137, 252, 235)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+115, 3249)-Net in Base 4 — Upper bound on s

There is no (137, 252, 3250)-net in base 4, because

1 times m-reduction [i] would yield (137, 251, 3250)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 153426 326896 395605 436779 418305 269419 043840 601280 513328 514097 136268 795298 028903 869898 225143 998487 757657 414148 320734 424405 441879 444144 808484 016243 349616 > 4²⁵¹ [i]