MinT - Best Known (108, 219, s)-Nets in Base 4

Best Known (108, 219, s)-Nets in Base 4

(108, 219, 130)-Net over F₄ — Constructive and digital

Digital (108, 219, 130)-net over F₄, using

t-expansion [i] based on digital (105, 219, 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]

(108, 219, 149)-Net over F₄ — Digital

Digital (108, 219, 149)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 219, 1686)-Net in Base 4 — Upper bound on s

There is no (108, 219, 1687)-net in base 4, because

1 times m-reduction [i] would yield (108, 218, 1687)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 180529 135852 774758 428017 446193 405628 690668 277259 511603 372044 212129 723281 883030 669284 858920 195244 914477 737115 582286 282443 104764 104880 > 4²¹⁸ [i]