MinT - Best Known (257−58, 257, s)-Nets in Base 4

Best Known (257−58, 257, s)-Nets in Base 4

(257−58, 257, 1052)-Net over F₄ — Constructive and digital

Digital (199, 257, 1052)-net over F₄, using

4¹ times duplication [i] based on digital (198, 256, 1052)-net over F₄, using
- trace code for nets [i] based on digital (6, 64, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(257−58, 257, 3843)-Net over F₄ — Digital

Digital (199, 257, 3843)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−58, 257, 842336)-Net in Base 4 — Upper bound on s

There is no (199, 257, 842337)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53631 738134 500329 123945 557032 257718 788665 066618 114588 683553 085959 619877 842098 694218 640466 998993 668599 676278 339592 379037 212104 643630 688424 900634 348228 886912 > 4²⁵⁷ [i]