MinT - Best Known (118, 118+135, s)-Nets in Base 4

Best Known (118, 118+135, s)-Nets in Base 4

(118, 118+135, 130)-Net over F₄ — Constructive and digital

Digital (118, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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+135, 168)-Net over F₄ — Digital

Digital (118, 253, 168)-net over F₄, using

t-expansion [i] based on digital (115, 253, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(118, 118+135, 1525)-Net in Base 4 — Upper bound on s

There is no (118, 253, 1526)-net in base 4, because

1 times m-reduction [i] would yield (118, 252, 1526)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53 257108 749988 934964 916406 458861 768424 527017 895942 233159 469625 103048 753810 827607 869364 377495 951863 697090 151830 308244 693995 830133 375174 054646 341521 231550 > 4²⁵² [i]