MinT - Best Known (218−91, 218, s)-Nets in Base 4

Best Known (218−91, 218, s)-Nets in Base 4

(218−91, 218, 130)-Net over F₄ — Constructive and digital

Digital (127, 218, 130)-net over F₄, using

t-expansion [i] based on digital (105, 218, 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]

(218−91, 218, 275)-Net over F₄ — Digital

Digital (127, 218, 275)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−91, 218, 4665)-Net in Base 4 — Upper bound on s

There is no (127, 218, 4666)-net in base 4, because

1 times m-reduction [i] would yield (127, 217, 4666)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44571 504833 233761 789652 688347 929832 324288 592465 412922 680087 633377 224445 851510 403726 156904 799131 424834 290164 680371 262848 051782 931148 > 4²¹⁷ [i]