MinT - Best Known (120, 120+131, s)-Nets in Base 4

Best Known (120, 120+131, s)-Nets in Base 4

(120, 120+131, 130)-Net over F₄ — Constructive and digital

Digital (120, 251, 130)-net over F₄, using

t-expansion [i] based on digital (105, 251, 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]

(120, 120+131, 168)-Net over F₄ — Digital

Digital (120, 251, 168)-net over F₄, using

t-expansion [i] based on digital (115, 251, 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]

(120, 120+131, 1673)-Net in Base 4 — Upper bound on s

There is no (120, 251, 1674)-net in base 4, because

1 times m-reduction [i] would yield (120, 250, 1674)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 320529 123762 838838 316275 129700 013252 617619 423115 747636 340150 883737 775324 605273 358969 212976 713881 699054 606428 286310 154012 113786 746083 300592 582486 955010 > 4²⁵⁰ [i]