MinT - Best Known (238−105, 238, s)-Nets in Base 4

Best Known (238−105, 238, s)-Nets in Base 4

(238−105, 238, 130)-Net over F₄ — Constructive and digital

Digital (133, 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]

(238−105, 238, 249)-Net over F₄ — Digital

Digital (133, 238, 249)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−105, 238, 3696)-Net in Base 4 — Upper bound on s

There is no (133, 238, 3697)-net in base 4, because

1 times m-reduction [i] would yield (133, 237, 3697)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49073 522891 255014 780834 196736 509111 655180 008947 322929 453514 458650 742938 282324 946028 177047 922469 034239 436915 660297 703496 332440 448486 562100 251280 > 4²³⁷ [i]