MinT - Best Known (250−123, 250, s)-Nets in Base 4

Best Known (250−123, 250, s)-Nets in Base 4

(250−123, 250, 130)-Net over F₄ — Constructive and digital

Digital (127, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 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]

(250−123, 250, 184)-Net over F₄ — Digital

Digital (127, 250, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−123, 250, 2202)-Net in Base 4 — Upper bound on s

There is no (127, 250, 2203)-net in base 4, because

1 times m-reduction [i] would yield (127, 249, 2203)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 824613 625704 100927 533832 710700 381526 770368 835784 146200 880685 166329 109686 411515 712361 763665 340713 382656 533378 841023 539098 367960 336185 655190 417237 310400 > 4²⁴⁹ [i]