MinT - Best Known (124, 124+136, s)-Nets in Base 4

Best Known (124, 124+136, s)-Nets in Base 4

(124, 124+136, 130)-Net over F₄ — Constructive and digital

Digital (124, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(124, 124+136, 168)-Net over F₄ — Digital

Digital (124, 260, 168)-net over F₄, using

t-expansion [i] based on digital (115, 260, 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]

(124, 124+136, 1692)-Net in Base 4 — Upper bound on s

There is no (124, 260, 1693)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 555240 163168 738946 158051 837889 540889 325944 449359 016408 943270 579282 681098 654350 719581 093412 891864 095367 907683 284782 575883 416694 639127 078878 685933 182286 859010 > 4²⁶⁰ [i]