MinT - Best Known (218−148, 218, s)-Nets in Base 4

Best Known (218−148, 218, s)-Nets in Base 4

(218−148, 218, 66)-Net over F₄ — Constructive and digital

Digital (70, 218, 66)-net over F₄, using

t-expansion [i] based on digital (49, 218, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(218−148, 218, 105)-Net over F₄ — Digital

Digital (70, 218, 105)-net over F₄, using

net from sequence [i] based on digital (70, 104)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
  - Drinfeld modules of rank 1 [i]

(218−148, 218, 502)-Net in Base 4 — Upper bound on s

There is no (70, 218, 503)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 179584 297583 748909 201378 975559 288007 047289 742310 082768 444938 003958 644462 404141 265447 584423 789053 257786 786325 450631 366209 624147 290306 > 4²¹⁸ [i]