MinT - Best Known (120, 219, s)-Nets in Base 4

Best Known (120, 219, s)-Nets in Base 4

(120, 219, 130)-Net over F₄ — Constructive and digital

Digital (120, 219, 130)-net over F₄, using

t-expansion [i] based on digital (105, 219, 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, 219, 214)-Net over F₄ — Digital

Digital (120, 219, 214)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 219, 2998)-Net in Base 4 — Upper bound on s

There is no (120, 219, 2999)-net in base 4, because

1 times m-reduction [i] would yield (120, 218, 2999)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177644 014570 081615 891182 467156 235753 564553 430967 288457 029354 286825 618607 752049 615600 736905 095695 240494 124638 715859 442168 018448 565894 > 4²¹⁸ [i]