MinT - Best Known (128−30, 128, s)-Nets in Base 4

Best Known (128−30, 128, s)-Nets in Base 4

(128−30, 128, 1036)-Net over F₄ — Constructive and digital

Digital (98, 128, 1036)-net over F₄, using

trace code for nets [i] based on digital (2, 32, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(128−30, 128, 1782)-Net over F₄ — Digital

Digital (98, 128, 1782)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−30, 128, 293904)-Net in Base 4 — Upper bound on s

There is no (98, 128, 293905)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 115794 997528 688644 701808 746682 187478 484443 121303 165698 414274 945264 618107 185104 > 4¹²⁸ [i]