MinT - Best Known (208−101, 208, s)-Nets in Base 4

Best Known (208−101, 208, s)-Nets in Base 4

(208−101, 208, 130)-Net over F₄ — Constructive and digital

Digital (107, 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]

(208−101, 208, 163)-Net over F₄ — Digital

Digital (107, 208, 163)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−101, 208, 1977)-Net in Base 4 — Upper bound on s

There is no (107, 208, 1978)-net in base 4, because

1 times m-reduction [i] would yield (107, 207, 1978)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42479 429820 991238 031279 593542 198766 643843 921000 815175 775998 486464 576672 636458 316517 947910 408953 071835 145412 571784 844951 789876 > 4²⁰⁷ [i]