MinT - Best Known (217−53, 217, s)-Nets in Base 4

Best Known (217−53, 217, s)-Nets in Base 4

(217−53, 217, 1032)-Net over F₄ — Constructive and digital

Digital (164, 217, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (163, 216, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 54, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(217−53, 217, 2220)-Net over F₄ — Digital

Digital (164, 217, 2220)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−53, 217, 353081)-Net in Base 4 — Upper bound on s

There is no (164, 217, 353082)-net in base 4, because

1 times m-reduction [i] would yield (164, 216, 353082)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11091 122502 571678 311464 944723 798478 104537 374607 288942 533389 181254 069718 206417 074434 814218 753544 170891 063981 978978 523032 995885 939656 > 4²¹⁶ [i]