MinT - Best Known (212−44, 212, s)-Nets in Base 4

Best Known (212−44, 212, s)-Nets in Base 4

(212−44, 212, 1064)-Net over F₄ — Constructive and digital

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]

(212−44, 212, 5253)-Net over F₄ — Digital

Digital (168, 212, 5253)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−44, 212, 1911598)-Net in Base 4 — Upper bound on s

There is no (168, 212, 1911599)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 323110 162506 341297 809676 095317 999898 502822 877071 776400 620309 328756 539111 205076 335663 598266 036385 064609 850860 067946 912558 504510 > 4²¹² [i]