MinT - Best Known (247−141, 247, s)-Nets in Base 4

Best Known (247−141, 247, s)-Nets in Base 4

(247−141, 247, 130)-Net over F₄ — Constructive and digital

Digital (106, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 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]

(247−141, 247, 144)-Net over F₄ — Digital

Digital (106, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 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]

(247−141, 247, 1113)-Net in Base 4 — Upper bound on s

There is no (106, 247, 1114)-net in base 4, because

1 times m-reduction [i] would yield (106, 246, 1114)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12974 940712 291977 391129 719086 720176 201584 970875 727487 100845 097597 765800 753649 051444 408114 276970 129555 348498 661166 730305 806023 270173 721441 064763 260236 > 4²⁴⁶ [i]