MinT - Best Known (238−113, 238, s)-Nets in Base 4

Best Known (238−113, 238, s)-Nets in Base 4

(238−113, 238, 130)-Net over F₄ — Constructive and digital

Digital (125, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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]

(238−113, 238, 197)-Net over F₄ — Digital

Digital (125, 238, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−113, 238, 2509)-Net in Base 4 — Upper bound on s

There is no (125, 238, 2510)-net in base 4, because

1 times m-reduction [i] would yield (125, 237, 2510)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48855 100689 029275 447875 342068 714465 359431 347883 211516 199996 627860 318802 088136 493309 861103 794762 760333 212384 017810 586903 329598 056046 114730 057172 > 4²³⁷ [i]