MinT - Best Known (203−90, 203, s)-Nets in Base 4

Best Known (203−90, 203, s)-Nets in Base 4

(203−90, 203, 130)-Net over F₄ — Constructive and digital

Digital (113, 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]

(203−90, 203, 213)-Net over F₄ — Digital

Digital (113, 203, 213)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−90, 203, 3018)-Net in Base 4 — Upper bound on s

There is no (113, 203, 3019)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 167 284283 869149 977859 382367 569330 524457 479844 637391 563674 992162 342329 784770 953299 224318 644933 638603 455715 840348 052603 203616 > 4²⁰³ [i]