MinT - Best Known (206−91, 206, s)-Nets in Base 4

Best Known (206−91, 206, s)-Nets in Base 4

(206−91, 206, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(206−91, 206, 218)-Net over F₄ — Digital

Digital (115, 206, 218)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−91, 206, 3212)-Net in Base 4 — Upper bound on s

There is no (115, 206, 3213)-net in base 4, because

1 times m-reduction [i] would yield (115, 205, 3213)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2669 509967 560981 674667 159618 775561 316962 316845 344507 756556 489704 382118 632825 893693 761445 742852 945267 538853 668508 538772 095728 > 4²⁰⁵ [i]