MinT - Best Known (226−120, 226, s)-Nets in Base 4

Best Known (226−120, 226, s)-Nets in Base 4

(226−120, 226, 130)-Net over F₄ — Constructive and digital

Digital (106, 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]

(226−120, 226, 144)-Net over F₄ — Digital

Digital (106, 226, 144)-net over F₄, using

t-expansion [i] based on digital (91, 226, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(226−120, 226, 1383)-Net in Base 4 — Upper bound on s

There is no (106, 226, 1384)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12003 131914 605432 551119 780734 040439 119771 786997 168294 994283 264206 512359 258866 023242 741681 256157 007380 004909 407377 716791 164704 790621 291560 > 4²²⁶ [i]