MinT - Best Known (167, 211, s)-Nets in Base 4

Best Known (167, 211, s)-Nets in Base 4

(167, 211, 1060)-Net over F₄ — Constructive and digital

Digital (167, 211, 1060)-net over F₄, using

1 times m-reduction [i] based on digital (167, 212, 1060)-net over F₄, using
- trace code for nets [i] based on digital (8, 53, 265)-net over F₂₅₆, using
  - net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(167, 211, 5087)-Net over F₄ — Digital

Digital (167, 211, 5087)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 211, 1794858)-Net in Base 4 — Upper bound on s

There is no (167, 211, 1794859)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 830870 358311 044325 471259 178921 721212 189563 502793 530693 442205 449634 272060 503797 254566 516348 706083 314182 384559 412787 523174 001980 > 4²¹¹ [i]