MinT - Best Known (109, 109+87, s)-Nets in Base 4

Best Known (109, 109+87, s)-Nets in Base 4

(109, 109+87, 130)-Net over F₄ — Constructive and digital

Digital (109, 196, 130)-net over F₄, using

t-expansion [i] based on digital (105, 196, 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]

(109, 109+87, 205)-Net over F₄ — Digital

Digital (109, 196, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+87, 2989)-Net in Base 4 — Upper bound on s

There is no (109, 196, 2990)-net in base 4, because

1 times m-reduction [i] would yield (109, 195, 2990)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2554 737778 560513 772892 195235 602120 411853 905022 464404 716477 005611 803557 625094 707472 326240 121967 223459 646243 008793 761610 > 4¹⁹⁵ [i]