MinT - Best Known (123, 258, s)-Nets in Base 4

Best Known (123, 258, s)-Nets in Base 4

(123, 258, 130)-Net over F₄ — Constructive and digital

Digital (123, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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]

(123, 258, 168)-Net over F₄ — Digital

Digital (123, 258, 168)-net over F₄, using

t-expansion [i] based on digital (115, 258, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(123, 258, 1697)-Net in Base 4 — Upper bound on s

There is no (123, 258, 1698)-net in base 4, because

1 times m-reduction [i] would yield (123, 257, 1698)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 54100 912206 758824 176560 847597 562066 920226 601869 859075 845915 165624 489817 166658 665395 440836 469691 192537 720676 358953 618309 039112 542797 340870 292910 771873 435584 > 4²⁵⁷ [i]