MinT - Best Known (243−108, 243, s)-Nets in Base 4

Best Known (243−108, 243, s)-Nets in Base 4

(243−108, 243, 130)-Net over F₄ — Constructive and digital

Digital (135, 243, 130)-net over F₄, using

t-expansion [i] based on digital (105, 243, 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]

(243−108, 243, 247)-Net over F₄ — Digital

Digital (135, 243, 247)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−108, 243, 3534)-Net in Base 4 — Upper bound on s

There is no (135, 243, 3535)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 202 423201 751558 009382 879626 988526 260603 344009 272806 297154 191781 618995 417165 683246 892721 108306 872145 303798 133902 577229 666163 131384 793552 634952 422260 > 4²⁴³ [i]