MinT - Best Known (249−123, 249, s)-Nets in Base 4

Best Known (249−123, 249, s)-Nets in Base 4

(249−123, 249, 130)-Net over F₄ — Constructive and digital

Digital (126, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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]

(249−123, 249, 181)-Net over F₄ — Digital

Digital (126, 249, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−123, 249, 2152)-Net in Base 4 — Upper bound on s

There is no (126, 249, 2153)-net in base 4, because

1 times m-reduction [i] would yield (126, 248, 2153)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209683 002019 674746 855324 490835 430299 891755 300886 515624 763194 416231 113228 661366 288494 483459 942591 167662 211830 480509 473162 106323 523398 684257 713965 001600 > 4²⁴⁸ [i]