MinT - Best Known (238−109, 238, s)-Nets in Base 4

Best Known (238−109, 238, s)-Nets in Base 4

(238−109, 238, 130)-Net over F₄ — Constructive and digital

Digital (129, 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]

(238−109, 238, 221)-Net over F₄ — Digital

Digital (129, 238, 221)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−109, 238, 3023)-Net in Base 4 — Upper bound on s

There is no (129, 238, 3024)-net in base 4, because

1 times m-reduction [i] would yield (129, 237, 3024)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49359 242914 876043 536915 881523 815165 064987 587745 508420 470181 114641 554499 249505 051979 906394 105208 910255 555740 721451 127513 566450 548982 037707 425964 > 4²³⁷ [i]