MinT - Best Known (121, 121+131, s)-Nets in Base 4

Best Known (121, 121+131, s)-Nets in Base 4

(121, 121+131, 130)-Net over F₄ — Constructive and digital

Digital (121, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(121, 121+131, 168)-Net over F₄ — Digital

Digital (121, 252, 168)-net over F₄, using

t-expansion [i] based on digital (115, 252, 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]

(121, 121+131, 1710)-Net in Base 4 — Upper bound on s

There is no (121, 252, 1711)-net in base 4, because

1 times m-reduction [i] would yield (121, 251, 1711)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 176692 956650 539922 090071 060400 058208 705302 579890 237492 425661 072968 908524 739038 278507 708672 142568 924824 108421 180969 361575 269892 435796 510184 448543 175020 > 4²⁵¹ [i]