MinT - Best Known (234−118, 234, s)-Nets in Base 4

Best Known (234−118, 234, s)-Nets in Base 4

(234−118, 234, 130)-Net over F₄ — Constructive and digital

Digital (116, 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]

(234−118, 234, 168)-Net over F₄ — Digital

Digital (116, 234, 168)-net over F₄, using

t-expansion [i] based on digital (115, 234, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(234−118, 234, 1809)-Net in Base 4 — Upper bound on s

There is no (116, 234, 1810)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 766 293198 750849 889206 582499 592886 542929 160230 229870 699192 332128 999169 198296 476889 285767 929498 977800 373623 616865 139142 128936 832088 702640 603776 > 4²³⁴ [i]