MinT - Best Known (159−65, 159, s)-Nets in Base 4

Best Known (159−65, 159, s)-Nets in Base 4

(159−65, 159, 130)-Net over F₄ — Constructive and digital

Digital (94, 159, 130)-net over F₄, using

17 times m-reduction [i] based on digital (94, 176, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 88, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(159−65, 159, 223)-Net over F₄ — Digital

Digital (94, 159, 223)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−65, 159, 3977)-Net in Base 4 — Upper bound on s

There is no (94, 159, 3978)-net in base 4, because

1 times m-reduction [i] would yield (94, 158, 3978)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 134236 257502 546154 491141 584712 992469 229000 810341 335275 826052 273308 112871 748843 232202 195121 686932 > 4¹⁵⁸ [i]