MinT - Best Known (250−145, 250, s)-Nets in Base 4

Best Known (250−145, 250, s)-Nets in Base 4

(250−145, 250, 130)-Net over F₄ — Constructive and digital

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]

(250−145, 250, 144)-Net over F₄ — Digital

Digital (105, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(250−145, 250, 1054)-Net in Base 4 — Upper bound on s

There is no (105, 250, 1055)-net in base 4, because

1 times m-reduction [i] would yield (105, 249, 1055)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 836301 000251 768924 435286 369155 284441 500193 503327 111093 242353 783090 623962 080588 675627 289733 717639 748845 621696 631361 190510 547935 601812 233395 501072 907248 > 4²⁴⁹ [i]