MinT - Best Known (238−117, 238, s)-Nets in Base 4

Best Known (238−117, 238, s)-Nets in Base 4

(238−117, 238, 130)-Net over F₄ — Constructive and digital

Digital (121, 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]

(238−117, 238, 177)-Net over F₄ — Digital

Digital (121, 238, 177)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−117, 238, 2111)-Net in Base 4 — Upper bound on s

There is no (121, 238, 2112)-net in base 4, because

1 times m-reduction [i] would yield (121, 237, 2112)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49381 707387 015733 115087 818434 398759 402629 322209 362197 791190 371731 658620 225214 782733 484108 814920 081428 390873 538555 167546 638143 356313 432952 697135 > 4²³⁷ [i]