MinT - Best Known (214−44, 214, s)-Nets in Base 4

Best Known (214−44, 214, s)-Nets in Base 4

(214−44, 214, 1064)-Net over F₄ — Constructive and digital

Digital (170, 214, 1064)-net over F₄, using

4² times duplication [i] based on digital (168, 212, 1064)-net over F₄, using
- trace code for nets [i] based on digital (9, 53, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(214−44, 214, 5601)-Net over F₄ — Digital

Digital (170, 214, 5601)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−44, 214, 2168352)-Net in Base 4 — Upper bound on s

There is no (170, 214, 2168353)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 693 169211 649694 764932 269936 422890 402461 186368 594188 358116 413842 297711 966548 829141 182864 283129 169066 108027 386486 592977 648335 700208 > 4²¹⁴ [i]