MinT - Best Known (234−111, 234, s)-Nets in Base 4

Best Known (234−111, 234, s)-Nets in Base 4

(234−111, 234, 130)-Net over F₄ — Constructive and digital

Digital (123, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(234−111, 234, 195)-Net over F₄ — Digital

Digital (123, 234, 195)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−111, 234, 2481)-Net in Base 4 — Upper bound on s

There is no (123, 234, 2482)-net in base 4, because

1 times m-reduction [i] would yield (123, 233, 2482)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 191 212213 039424 967205 538788 207349 201737 279325 618944 654324 343633 565766 115425 549639 752558 393345 072958 053755 916467 580982 256127 531374 491563 623872 > 4²³³ [i]