MinT - Best Known (203−89, 203, s)-Nets in Base 4

Best Known (203−89, 203, s)-Nets in Base 4

(203−89, 203, 130)-Net over F₄ — Constructive and digital

Digital (114, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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]

(203−89, 203, 220)-Net over F₄ — Digital

Digital (114, 203, 220)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−89, 203, 3304)-Net in Base 4 — Upper bound on s

There is no (114, 203, 3305)-net in base 4, because

1 times m-reduction [i] would yield (114, 202, 3305)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 629503 513953 508304 387394 736249 336328 533073 010614 179743 662921 206708 941752 930529 048996 293639 257535 078102 851041 067222 230800 > 4²⁰² [i]