MinT - Best Known (109, 206, s)-Nets in Base 4

Best Known (109, 206, s)-Nets in Base 4

(109, 206, 130)-Net over F₄ — Constructive and digital

Digital (109, 206, 130)-net over F₄, using

t-expansion [i] based on digital (105, 206, 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, 206, 178)-Net over F₄ — Digital

Digital (109, 206, 178)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 206, 2288)-Net in Base 4 — Upper bound on s

There is no (109, 206, 2289)-net in base 4, because

1 times m-reduction [i] would yield (109, 205, 2289)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2662 533312 289021 376388 345533 509198 737944 160068 395949 793350 313625 923422 901798 448286 219243 989536 443203 099410 361951 319787 796399 > 4²⁰⁵ [i]