MinT - Best Known (205−91, 205, s)-Nets in Base 4

Best Known (205−91, 205, s)-Nets in Base 4

(205−91, 205, 130)-Net over F₄ — Constructive and digital

Digital (114, 205, 130)-net over F₄, using

t-expansion [i] based on digital (105, 205, 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]

(205−91, 205, 214)-Net over F₄ — Digital

Digital (114, 205, 214)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−91, 205, 3113)-Net in Base 4 — Upper bound on s

There is no (114, 205, 3114)-net in base 4, because

1 times m-reduction [i] would yield (114, 204, 3114)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 663 433031 572184 125454 019584 698944 283451 767953 342554 534704 359442 868972 211908 336428 843499 664035 006207 056140 227941 001218 817536 > 4²⁰⁴ [i]