MinT - Best Known (123, 123+97, s)-Nets in Base 4

Best Known (123, 123+97, s)-Nets in Base 4

(123, 123+97, 130)-Net over F₄ — Constructive and digital

Digital (123, 220, 130)-net over F₄, using

t-expansion [i] based on digital (105, 220, 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, 123+97, 232)-Net over F₄ — Digital

Digital (123, 220, 232)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+97, 3448)-Net in Base 4 — Upper bound on s

There is no (123, 220, 3449)-net in base 4, because

1 times m-reduction [i] would yield (123, 219, 3449)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 713761 896974 517370 939436 415782 435722 400023 710799 621600 616289 388584 725638 174676 727701 492729 594880 007644 370949 556473 342060 468656 319905 > 4²¹⁹ [i]