MinT - Best Known (157, 197, s)-Nets in Base 4

Best Known (157, 197, s)-Nets in Base 4

(157, 197, 1064)-Net over F₄ — Constructive and digital

Digital (157, 197, 1064)-net over F₄, using

4¹ times duplication [i] based on digital (156, 196, 1064)-net over F₄, using
- trace code for nets [i] based on digital (9, 49, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(157, 197, 5662)-Net over F₄ — Digital

Digital (157, 197, 5662)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 197, 2357615)-Net in Base 4 — Upper bound on s

There is no (157, 197, 2357616)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40347 947038 099431 234265 746767 935376 726386 580329 539776 969619 983938 301904 606486 781393 520855 452256 562227 476542 127192 921894 > 4¹⁹⁷ [i]