MinT - Best Known (115, 115+127, s)-Nets in Base 4

Best Known (115, 115+127, s)-Nets in Base 4

(115, 115+127, 130)-Net over F₄ — Constructive and digital

Digital (115, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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]

(115, 115+127, 168)-Net over F₄ — Digital

Digital (115, 242, 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]

(115, 115+127, 1576)-Net in Base 4 — Upper bound on s

There is no (115, 242, 1577)-net in base 4, because

1 times m-reduction [i] would yield (115, 241, 1577)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 645932 461761 368868 725800 800553 607421 531116 165298 254001 218927 443027 275384 696446 568234 580069 336597 206862 403629 716612 547337 713688 753793 207122 859520 > 4²⁴¹ [i]