MinT - Best Known (218−146, 218, s)-Nets in Base 4

Best Known (218−146, 218, s)-Nets in Base 4

(218−146, 218, 66)-Net over F₄ — Constructive and digital

Digital (72, 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]

(218−146, 218, 105)-Net over F₄ — Digital

Digital (72, 218, 105)-net over F₄, using

t-expansion [i] based on 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]

(218−146, 218, 528)-Net in Base 4 — Upper bound on s

There is no (72, 218, 529)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 197168 181845 789375 480931 453190 998004 153164 111950 556621 218326 556093 930291 183481 195218 044144 265263 713135 428457 798570 649938 018341 644480 > 4²¹⁸ [i]