MinT - Best Known (121, 121+87, s)-Nets in Base 4

Best Known (121, 121+87, s)-Nets in Base 4

(121, 121+87, 130)-Net over F₄ — Constructive and digital

Digital (121, 208, 130)-net over F₄, using

t-expansion [i] based on digital (105, 208, 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+87, 262)-Net over F₄ — Digital

Digital (121, 208, 262)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+87, 4417)-Net in Base 4 — Upper bound on s

There is no (121, 208, 4418)-net in base 4, because

1 times m-reduction [i] would yield (121, 207, 4418)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42470 024961 831881 418535 516538 291602 875690 992176 718632 107621 897622 894130 488320 703825 570007 007783 971019 533575 765384 695884 244640 > 4²⁰⁷ [i]