MinT - Best Known (118, 118+83, s)-Nets in Base 4

Best Known (118, 118+83, s)-Nets in Base 4

(118, 118+83, 130)-Net over F₄ — Constructive and digital

Digital (118, 201, 130)-net over F₄, using

t-expansion [i] based on digital (105, 201, 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]

(118, 118+83, 265)-Net over F₄ — Digital

Digital (118, 201, 265)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+83, 4618)-Net in Base 4 — Upper bound on s

There is no (118, 201, 4619)-net in base 4, because

1 times m-reduction [i] would yield (118, 200, 4619)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 588010 598818 108645 234768 819058 062501 020032 507331 708647 570393 172202 043246 561914 830173 184214 476745 002255 869557 230160 951136 > 4²⁰⁰ [i]