MinT - Best Known (253−62, 253, s)-Nets in Base 4

Best Known (253−62, 253, s)-Nets in Base 4

(253−62, 253, 1032)-Net over F₄ — Constructive and digital

Digital (191, 253, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (190, 252, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 63, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(253−62, 253, 2497)-Net over F₄ — Digital

Digital (191, 253, 2497)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−62, 253, 339207)-Net in Base 4 — Upper bound on s

There is no (191, 253, 339208)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209 503466 070423 838185 035905 647286 796912 973547 416566 337878 153284 820597 383095 148442 612467 215031 593154 954220 209898 890370 467915 236347 750240 008353 883052 465440 > 4²⁵³ [i]