MinT - Best Known (226−116, 226, s)-Nets in Base 4

Best Known (226−116, 226, s)-Nets in Base 4

(226−116, 226, 130)-Net over F₄ — Constructive and digital

Digital (110, 226, 130)-net over F₄, using

t-expansion [i] based on digital (105, 226, 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]

(226−116, 226, 165)-Net over F₄ — Digital

Digital (110, 226, 165)-net over F₄, using

t-expansion [i] based on digital (109, 226, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(226−116, 226, 1612)-Net in Base 4 — Upper bound on s

There is no (110, 226, 1613)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11827 756759 372020 991883 309132 611939 194166 034791 013688 808537 420061 358496 310098 893871 669617 710957 890908 375205 049072 625235 026159 088452 871720 > 4²²⁶ [i]